The Nature of Mathematical Reasoning

80-110

Second Summer Session of 1998

Monday through Friday 1:30pm to 2:50pm





Class Description


What is mathematical reasoning? Can mathematical thinking expand the limits of our imagination or focus our daily activities? How does pure mathematics differ from other ways of thinking? Why are we so certain 1+2=3?

We begin exploring math not as a tool, but as something intrinsically interesting. Arithmetic, geometry, and logic illustrate the key ideas underlying modern math. We see mathematical thinking's influence. Mathematical precision can illuminate the infinite, analyze decisions, and perform computer processes. We also compare scientific and mathematical reasoning. Mathematicians and scientists induce generalizations differently. Cognitive scientists and linguists study language differently. In the concluding weeks, our understanding deepens with additional philosophical issues.

Humanities and art majors consider the big picture of math intriguing. Beginning math majors find this course a useful framework for future study. Science majors, with futures using math, see why math works.





Class Web Pages


  • Overview of the Class
  • Notes
    • Definitions and Peano Arithmetic
    • Axioms and Euclid's Elements
    • Truth Tables and the Implication Symbol
    • Why Mathematical Induction Works
    • Pascal's Wager (primary text)
    • St Anselm's Ontological Proof of the Existence of God and
      Gaunilo's Perfect Island Counterexample (primary text)
    • First Take Home Exam
    • Second Take Home Exam
  • Interesting Links
    • Euclid's Elements
    • fun math links
    • fun philosophy links
    • links relevant to particular class topics
  • About the Instructor





If you have any questions, please feel free to contact me. My e-mail address is grobman+@andrew.cmu.edu. My office is 143 Baker Hall and the phone number there is 268-8148.





please send questions to Kevin Grobman
Main Page for The Nature of Mathematical Reasoning